Finite Group Databasebeta

← #30603437

Subgroups — #30603437

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840706C211yesmaximal, characteristic
2C2×#16840635C212yesmaximal
3C2×#16840635C212yesmaximal
4#21461480C211yesmaximal, characteristic
5#389×D61C211yesmaximal, characteristic
6C22×D61⋊C8C2212yes—
7C22×C4⋊#6923C2212yes—
8#16840706—24no—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4—21no—
11#16840635—24no—
12#16840635—24no—
13#16840628—21no—
14#16840628—21no—
15C2×C4⋊C4×D61—21no—
16C2×C4⋊C4×D61C2211yescharacteristic
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19#16839661C411yescharacteristic, complemented
20#16839660C411yescharacteristic, complemented
21#16839659—21no—
22#16839658C411yescharacteristic, complemented
23#16839657—21no—
24#95×D61—21no—
25C61×#389C411yescharacteristic, complemented
26C23×#6923—22no—
27C2×D61⋊C8—22no—
28C2×D61⋊C8—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—22no—
31C2×D61⋊C8—22no—
32C2×D61⋊C8Q814yes—
33C22×#92420—22no—
34C2×C4⋊#6923—22no—
35C2×C4⋊#6923—22no—
36C2×C4⋊#6923—22no—
37C2×C4⋊#6923—22no—
38C2×C4⋊#6923—22no—
39C2×C4⋊#6923D414yes—
40(C2×#6923)⋊C4—24no—
41(C2×#6923)⋊C4—24no—
42C22×C4×D61—21no—
43C22×C4×D61—21no—
44C22×C4×D61D411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C22×C4×D61C2311yescharacteristic
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×C4⋊Dic61C2×C411yescharacteristic
50C2×#11758196—21no—
51C2×#11758196—21no—
52C2×#11758196—21no—
53C2×#11758196—21no—
54C4⋊C4×D61—21no—
55C4⋊C4×D61—21no—
56C4⋊C4×D61—22no—
57C4⋊C4×D61—22no—
58C4⋊C4×D61—44no—
59C4⋊C4×D61D412yes—
60C4⋊C4×D61Q812yes—
61C2×C4×Dic61C2×C411yescharacteristic
62C2×C4×Dic61D411yescharacteristic
63C2×C4×Dic61D411yescharacteristic
64C42×D61—22no—
65C42×D61—22no—
66#14519684—21no—
67#14519684—21no—
68#14519684—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C42×C61C2×C411yescharacteristic
73#95×C61—21no—
74C23×D61C2×D411yescharacteristic
75C22×#6923—24no—
76C22×#6923—42no—
77C22×#6923—42no—
78C22×#6923—42no—
79C22×#6923—42no—
80C22×#6923—42no—
81C22×#6923—42no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22⋊C411yescharacteristic
86C22×C4×C61C22×C411yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C2×C4×D61—21no—
93C2×C4×D61—21no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—22no—
99C2×C4×D61—22no—
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—41no—
105C2×C4×D61—41no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61C2×D411yescharacteristic
109C2×C4×D61C2×D412yes—
110C2×C4×D61C2×Q812yes—
111C2×C4×D61C2×Q811yescharacteristic
112C2×C4×D61#4112yes—
113C2×C4×D61#4111yescharacteristic
114C2×C4×D61#4112yes—
115C2×C4×D61#4111yescharacteristic
116C2×#92420—24no—
117C2×#92420—42no—
118C2×#92420—42no—
119C4⋊#6923—24no—
120C4⋊#6923—24no—
121C4⋊#6923—42no—
122C4⋊#6923—42no—
123D61⋊C8—24no—
124D61⋊C8—24no—
125D61⋊C8—42no—
126D61⋊C8—42no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—42no—
130C4⋊C4×C61C4⋊C412yes—
131C42×C61—22no—
132C4⋊Dic61—21no—
133C4⋊Dic61—22no—
134C4⋊Dic61—42no—
135C4⋊Dic61C4⋊C412yes—
136#11758196—22no—
137#11758196—22no—
138#11758196—42no—
139#11758196—42no—
140#11758196—42no—
141C4×Dic61—22no—
142C4×Dic61—22no—
143C4×Dic61—22no—
144C23×C61C2×C22⋊C411yescharacteristic
145C22×D61#12011yescharacteristic
146C22×D61#12111yescharacteristic
147C22×D61C22⋊Q811yescharacteristic
148C22×D61#12311yescharacteristic
149C22×D61#12411yescharacteristic
150C22×D61C4⋊Q811yescharacteristic
151C22×D61#13512yes—
152C22×D61#13512yes—
153C22×D61AGL(1,ℤ/8)12yes—
154C22×D61#13712yes—
155C2×#6923—44no—
156C2×#6923—44no—
157C2×#6923—44no—
158C2×#6923—82no—
159C2×#6923—82no—
160C2×#6923—82no—
161C2×#6923—82no—
162C2×C4×C61—22no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61C2×C4⋊C411yescharacteristic
175C2×C4×C61#11711yescharacteristic
176C2×C4×C61C4×D412yes—
177C2×C4×C61C4×Q812yes—
178C2×Dic61—22no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61#12111yescharacteristic
191C2×Dic61#12112yes—
192C2×Dic61C22⋊Q812yes—
193C2×Dic61C22⋊Q811yescharacteristic
194C4×D61—42no—
195C4×D61—42no—
196C4×D61—44no—
197C4×D61—44no—
198C4×D61—42no—
199C4×D61—42no—
200C4×D61—82no—
201C4×D61—82no—
202C4×D61#12112yes—
203C4×D61C22⋊Q812yes—
204C4×D61C22⋊Q812yes—
205C4×D61#12312yes—
206C4×D61#12512yes—
207C4×D61#12512yes—
208C4×D61#12612yes—
209C4×D61C4⋊Q812yes—
210#92420—44no—
211#11208—611nomaximal, Sylow
212C22×C61#38011yescharacteristic
213C22×C61#38611yescharacteristic
214C22×C61#39111yescharacteristic
215C22×C61#41611yescharacteristic
216C22×C61#41611yescharacteristic
217C22×C61#41811yescharacteristic
218C22×C61#41911yescharacteristic
219C2×D61#39411yescharacteristic
220C2×D61#39511yescharacteristic
221C2×D61#39811yescharacteristic
222C2×D61#40011yescharacteristic
223C2×D61#44912yes—
224C2×D61#45212yes—
225C2×D61#46312yes—
226C2×D61#46412yes—
227C2×D61#47812yes—
228C2×D61#47912yes—
229C2×D61#48212yes—
230C2×D61#48512yes—
231C2×D61#48812yes—
232C2×D61#48912yes—
233C2×D61#49912yes—
234C2×D61#50112yes—
235#6923—84no—
236C4×C61—42no—
237C4×C61—41no—
238C4×C61—41no—
239C4×C61—81no—
240C4×C61#38712yes—
241C4×C61#38912yes—
242Dic61—42no—
243Dic61—41no—
244Dic61—41no—
245Dic61—81no—
246Dic61#39612yes—
247Dic61#39812yes—
248C2×#389—611no—
249C2×#382—611no—
250C2×#340—612no—
251C2×#340—612no—
252C2×#336—611no—
253C2×C61#144111yescharacteristic
254C2×C61#180411yescharacteristic
255C2×C61#180511yescharacteristic
256C2×C61#187311yescharacteristic
257C2×C61#187511yescharacteristic
258C2×C61#199111yescharacteristic
259C2×C61#199311yescharacteristic
260D61#204212yes—
261D61#205912yes—
262D61#208512yes—
263D61#210112yes—
264C23×C8—612no—
265C22×C4⋊C4—611no—
266C22×C4⋊C4—612no—
267C22×C4⋊C4—611no—
268C22×C4⋊C4—1221no—
269C22×C42—611no—
270#389—611no—
271#389—611no—
272#389—611no—
273#389—1221no—
274#389—1221no—
275#389#692311yescharacteristic, complemented
276#382—1224no—
277C2×#95—1221no—
278C2×#95—1221no—
279C2×#95—1221no—
280#340—1224no—
281#340—1224no—
282#336—1221no—
283#336—1221no—
284C61#1120811yescharacteristic, complemented, Sylow
285C23×C4—611no—
286C23×C4—611no—
287C23×C4—611no—
288C23×C4—1221no—
289C23×C4—1221no—
290C23×C4—1222no—
291C22×C8—614no—
292C22×C8—1222no—
293C22×C8—1222no—
294C22×C8—1222no—
295C22×C8—1222no—
296C22×C8—1222no—
297C22×C8—1222no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—612no—
301C2×C4⋊C4—612no—
302C2×C4⋊C4—614no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1222no—
307C2×C4⋊C4—1222no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1222no—
310C2×C4⋊C4—1222no—
311C2×C4⋊C4—1222no—
312C2×C4⋊C4—1222no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1222no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4—2444no—
319C2×C4⋊C4C2×#692311yescharacteristic
320C2×C4⋊C4C2×#692311yescharacteristic
321C2×C42—611no—
322C2×C42—611no—
323C2×C42—611no—
324C2×C42—1222no—
325C2×C42—1222no—
326C2×C42C2×#692311yescharacteristic
327#95—21no—
328#95—1221no—
329#95—1221no—
330#95—1224no—
331#95—1224no—
332#95—1221no—
333C24—611no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—611no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—612no—
342C22×C4—612no—
343C22×C4—612no—
344C22×C4—612no—
345C22×C4—611no—
346C22×C4—611no—
347C22×C4—1221no—
348C22×C4—1221no—
349C22×C4—1221no—
350C22×C4—1221no—
351C22×C4—1222no—
352C22×C4—1222no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1221no—
358C22×C4—1224no—
359C22×C4—1221no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4—2442no—
366C22×C4—2442no—
367C22×C4—2442no—
368C22×C4—2442no—
369C22×C4—2442no—
370C22×C4—2442no—
371C22×C4—2442no—
372C22×C4C22⋊#692311yescharacteristic
373C22×C4C22⋊#692311yescharacteristic
374C22×C4C22×#692311yescharacteristic
375C2×C8—1224no—
376C2×C8—1224no—
377C2×C8—1224no—
378C2×C8—2442no—
379C2×C8—2442no—
380C2×C8—2442no—
381C2×C8—2442no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—42no—
385C4⋊C4—612no—
386C4⋊C4—1222no—
387C4⋊C4—1222no—
388C4⋊C4—1224no—
389C4⋊C4—1224no—
390C4⋊C4—1221no—
391C4⋊C4—1222no—
392C4⋊C4—2442no—
393C4⋊C4—2442no—
394C4⋊C4—2442no—
395C4⋊C4—2442no—
396C4⋊C4—2442no—
397C4⋊C4—2442no—
398C4⋊C4C4⋊#692312yes—
399C42—22no—
400C42—1222no—
401C42—1222no—
402C42—1222no—
403C23—611no—
404C23—611no—
405C23—611no—
406C23—611no—
407C23—611no—
408C23—611no—
409C23—612no—
410C23—612no—
411C23—612no—
412C23—612no—
413C23C2×C22⋊#692311yescharacteristic
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—611no—
427C2×C4—611no—
428C2×C4—612no—
429C2×C4—612no—
430C2×C4—612no—
431C2×C4—612no—
432C2×C4—612no—
433C2×C4—612no—
434C2×C4—612no—
435C2×C4—612no—
436C2×C4—612no—
437C2×C4—612no—
438C2×C4—1222no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—1221no—
445C2×C4—4882no—
446C2×C4—4882no—
447C2×C4—4882no—
448C2×C4—4882no—
449C2×C4—4882no—
450C2×C4—4882no—
451C2×C4—2442no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2444no—
456C2×C4—2444no—
457C2×C4—2444no—
458C2×C4—2444no—
459C2×C4—2444no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4C2×C4⋊#692311yescharacteristic
466C2×C4#1451985611yescharacteristic
467C2×C4D4×#692312yes—
468C2×C4Q8×#692312yes—
469C8—2444no—
470C22—611no—
471C22—611no—
472C22—611no—
473C22—611no—
474C22—612no—
475C22—612no—
476C22—612no—
477C22—612no—
478C22—612no—
479C22—612no—
480C22—612no—
481C22—612no—
482C22—612no—
483C22—612no—
484C22—612no—
485C22—612no—
486C22#1684070411yescharacteristic
487C22#1684071011yescharacteristic
488C22(C2×#6923)⋊Q811yescharacteristic
489C22#1684075211yescharacteristic
490C22#1684075211yescharacteristic
491C22#1684075411yescharacteristic
492C22#1684075511yescharacteristic
493C4—41no—
494C4—41no—
495C4—42no—
496C4—81no—
497C4—612no—
498C4—612no—
499C4—4884no—
500C4—4881no—
501C4—2441no—
502C4—2441no—
503C4—2442no—
504C4#1684071112yes—
505C4#1684071312yes—
506C2—612no—
507C2—612no—
508C2—612no—
509C2—612no—
510C2#2146100411yescharacteristic
511C2#2146168911yescharacteristic
512C2#2146169011yescharacteristic
513C2#2146180511yescharacteristic
514C2#2146180711yescharacteristic
515C2#2146200111yescharacteristic
516C2#2146200311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#389C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#389#6923
hypocenterC61#11208
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
19. #16839661C4semidirect
20. #16839660C4semidirect
22. #16839658C4semidirect
25. C61×#389C4semidirect
275. #389#6923semidirect
284. C61#11208semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168407062
C2×#168406352
#214614802
#389×D612
#1120861